Decidable Reasoning in a First-Order Logic of Limited Conditional Belief

In a series of papers, Liu, Lakemeyer, and Levesque address the problem of decidable reasoning in expressive first-order knowledge bases. Here, we extend their ideas to accommodate conditional beliefs, as in "if she is Australian, then she presumably eats Kangaroo meat." Perhaps the most prevalent semantics of a conditional belief is to evaluate the consequent in the most-plausible worlds consistent with the premise. In this paper, we devise a technique to approximate this notion of plausibility, and complement it with Liu, Lakemeyer, and Levesque's weak inference. Based on these ideas, we develop a logic of limited conditional belief, and provide soundness, decidability, and (for the propositional case) tractability results.